The present invention relates generally to cellular and wireless communication and, more particularly, to an equalizer hypothesizing modulation symbols received over multipath fading channels.
Signals in a wireless communication system are subject to a number of phenomena that degrade signal quality. Each signal is reflected from many different man-made and natural objects. The receiver thus receives a number of signals delayed by one or more signal periods, called xe2x80x9cmultipathxe2x80x9d, as each reflected signal is received. If the period of delay is more than the time required to transmit one symbol, producing intersymbol interference (ISI), then a receiver decoder may not be able to decode the symbol. This can cause poor sound or data quality to the user. Many different algorithms are used at the receiver to attempt to compensate for such effects. These techniques are discussed, for example, by G. L. Stxc3xcber in Principles of Mobile Communication, Chapter 6, Kluwer Academic Publishers, 1996. One such algorithm is the maximum likelihood sequence estimation (MLSE) or xe2x80x9cViterbixe2x80x9d algorithm.
Digital cellular and personal communication systems based on IS-136 and GSM (global system for mobile communications) require equalization to handle ISI arising from time dispersion. With the advent of the high date rates and the high level modulation in EDGE (enhanced data rates for global evolution) systems, the extent of ISI has increased considerably. To cover the same delay spread as today""s GSM, EDGE receivers are specified to resolve a 5-tap channel. Furthermore, these systems are convolutional coded. To enable soft-decision decoding, it is, therefore, highly desirable for the equalizers to produce soft information at the bit level.
For M-ary modulation, a traditional MLSE equalizer requires ML at each trellis stage in order to properly model an intersymbol interference (ISI) channel driven by L+1 M-ary phase-shift keying (MPSK) symbols. Because of the high computational and storage requirements this implies, the delayed decision feedback sequence estimation (DDFSE) equalizer uses a kind of hybrid of MLSE and DFE (decision feedback estimation) in which only the K+1 most recent symbols are hypothesized as part of the state model, while the remaining Lxe2x88x92K symbols required to compute each path metrics are determines from the surviving paths of each state. Therefore, a trellis of only MK states is needed in this case and the Lxe2x88x92K xe2x80x9cDFExe2x80x9d symbols constitute side information of the states. DDFSE equalizers are discussed, for example, by A. Duel-Hallen and C. Heegard in xe2x80x9cDelayed Decision Feedback Sequence Estimation,xe2x80x9d IEEE Transactions on Communications, vol. 37, no. 5, pp. 428-436, May 1989. One convenient way of describing the DDFSE operation is to say that the energy in the most recent K+1 xe2x80x9cMLSExe2x80x9d symbols is used to equalize the data, while the energy in the remaining xe2x80x9cDFExe2x80x9d symbols is simply canceled. The performance of DDFSE equalizers can be improved by pre-filtering the received signals with minimum-phase filters to maximize the energy of the leading ISI taps. Such filtering techniques are discussed, for example, in application Ser. No. 09/378,314 entitled xe2x80x9cMethod and Apparatus for Computing Prefilter Coefficientsxe2x80x9d of K. C. Zangi et al. and filed Aug 20, 1999.
In a convolutional coded system, a Log-MAP (maximum a posteriori) equalizer is preferred because of its ability to generate high-quality soft information for the Viterbi decoder. Traditional MAP algorithms, as described in L. R. Bahl, J. Cocke, F. Jelinek and J. Raviv (BCJR) in xe2x80x9cOptimal Decoding of Linear Codes for Minimizing Symbol Error Rate,xe2x80x9d IEEE Transactions on Information Theory, vol. 20, pp.284-287, March 1974, are not very suited to practical implementation because these algorithms require many multiplication and logarithm operations. The Log-MAP algorithms circumvent this complexity problem by operating the signals in the logarithmic domain, as discussed, for example, by P. Robertson, E. Villebrun and P. Hoehner, in xe2x80x9cA Comparison of Optimal and Sub-Optimal MAP decoding algorithms operating in the log domain,xe2x80x9d Proceedings of IEEE International Communications Conference""95, pp. 1009-1013, June 1995. However, both approaches are designed to generate optimal soft information for trellis with static state spaces, i.e., the definitions of the states do not change over time. Moreover, these definitions are known a priori and are usually given exogenously. For example, the trellis of a convolutional code falls into this category: the states are defined by the contents of the encoding shift-registers and the complete trellis can be constructed even before the codewords are transmitted. For multipath equalization, the traditional MAP algorithms thus require the construction of the complete state space as in the case for MLSE equalizers. For many practical applications, this proves to be excessively complex. For example, a MAP equalizer for 8PSK with 5 channel taps (EDGE specifications) requires 4096 states.
Since the Log-MAP equalizers suffer from the same complexity problems as the MLSE equalizers, it would be of great practical value if the principle of DDFSE could be combined with the Log-MAP algorithms to reduce complexity. An approach to this problem is discussed in the following.
Several problems arise when this MLSE/DFE hybrid method is applied to a forward-backward Log-MAP equalizer. More specifically, the forward DDFSE recursion would use an anti-causal prefilter to create a minimum-phase channel response. A DDFSE run backwards through the trellis, on the other hand, would need a causal prefilter to crease a maximum-phase channel, because in this case the MLSE symbols appear at the other end of the true state, as illustrated in FIG. 1. This results in two major issues:
1. The forward-backward Log-MAP algorithm breaks down. The two passes are now using two sets of data which are correlated with each other (because of the two prefilters with overlapping support). Because of this correlation, the Markovian property of the data sequence, which means that the future data symbols are independent of the past data symbols given the current state, no longer holds. This Markovian property plays an essential role in the derivation of the forward-backward algorithm, without which the Log-MAP algorithm is invalid.
2. The state space from the two recursions do not match. A complete state space is used in a Log-MAP equalizer, which guarantees the forward and backward recursions work on the same state space. On the other hand, for a naive delayed decision feedback Log-MAP equalizer, only the xe2x80x9cMLSExe2x80x9d symbols can be matched up. The xe2x80x9cDFExe2x80x9d symbols setup by the forward and backward recursions generally do not agree with each other. The overlapping supports of the two prefilters makes the situation even more confusing.
The definitions of the states in a DDFSE trellis are constructed endogenously by the equalization recursion itself and, therefore, become unknown a priori. The traditional MAP algorithms are thus not directly applicable in these situations. In order to extract soft information, ad hoc post-processing methods such as the soft-output Viterbi algorithms (SOVA) are usually used instead. The SOVA algorithm is discussed, for example, by J. Jagenauer and P. Hoehner in xe2x80x9cA Viterbi Algorithm with Soft-Decision Outputs and its Applications,xe2x80x9d Proceedings of IEEE Global Telecommunications Conference""89, pp. 1680-1686, November 1989. These algorithms, however, are sub-optimal and their shortcomings become more apparent in iterative processing settings.
Accordingly, there is a need for an equalizer and method that generates optimal soft information at the bit level for MPSK and MDPSK modulations over multipath fading channels.
The present invention meets this need by providing a delayed decision feedback Log-MAP equalizer that generates optimal soft information at the bit level for MPSK and MDPSK modulations over multipath fading channels.
Broadly, there is disclosed in accordance with one aspect of the invention a method of hypothesizing modulation symbols received over multipath fading channels. An estimate of a received sequence of symbols is calculated and stored using stored channel coefficients and a previous state path history of modulation symbols. For each possible current state symbol, a branch metric is calculated and stored from a prior state to a current state using the calculated estimate of the received sequence of symbols. A forward recursion is performed by calculating a forward state metric using the branch metric from the prior state to the current state. A backward recursion is performed by calculating a backward state metric using the branch metric from the prior state to the current state.
It is a feature of the invention that the estimate of a received sequence of symbols calculated and stored using stored channel coefficients and a previous state path history of modulation symbols is implemented using a delayed decision feedback sequence estimation equalizer.
It is another feature of the invention that the estimate of a received sequence of symbols calculated and stored using stored channel coefficients and a previous state path history of modulation symbols is implemented using a maximum likelihood sequence estimation equalizer for most recent symbols in the sequence of symbols and using a decision feedback equalizer for remaining symbols in the sequence of symbols.
It is a further feature of the invention that a Log-MAP equalizer is used to calculate and store the branch metric, the forward state metric and the backward state metric.
It is yet another feature of the invention that a posteriori log-likelihood ratio of each bit in the hypothesized modulation symbols is calculated using the calculated forward state metric and the calculated backward state metric.
It is still another feature of the invention that the forward recursion is executed prior to the backward recursion.
It is still an additional feature of the invention that the backward recursion is executed prior to the forward recursion.
It is yet still another feature of the invention that the previous state path history of modulation symbols is updated using the calculated branch metric from a prior state to a current state using the calculated estimate of the received sequence of symbols.
It is still a further feature of the invention that the modulation symbols received over multipath fading channels comprise M-ary modulated symbols.
It is yet a further feature of the invention that the modulation symbols received over multipath fading channels comprise M-ary differential PSK modulated symbols.
There is disclosed in accordance with another aspect of the invention, in a receiver receiving modulation symbols transmitted over multipath fading channels, an equalizer including a programmed controller. The programmed controller calculates and stores an estimate of a received sequence of symbols using stored channel coefficients and a previous state path history of modulation symbols. A branch metric is calculated and stored for each possible current state symbol from a prior state to a current state using the calculated estimate of the received sequence of symbols. A forward recursion is performed by calculating a forward state metric using the branch metric from the prior state to the current state. A backward recursion is performed by calculating a backward state metric using the branch metric from the prior state to the current state.
There is disclosed in accordance with a further aspect of the invention a method of generating soft information at bit level of modulation symbols received over multipath fading channels. An estimate of a received sequence of symbols is calculated and stored using stored channel coefficients and a previous state path history of modulation symbols, each symbol comprising an M-ary modulated symbol representing select bits c. A branch metric for each possible current state symbol is calculated and stored from a prior state to a current state using the calculated estimate of the received sequence of symbols. A forward recursion is performed by calculating a forward state metric using the branch metric from the prior state to the current state. A backward recursion is performed by calculating a backward state metric using the branch metric from the prior state to the current state. A posteriori log-likelihood ratio of each select bit c in the estimated modulation symbols is calculated using the calculated forward state metric and the calculated backward state metric.
Particularly, a DDFSE method is incorporated with a forward recursion to construct a reduced state space. Starting with a complete state space, the ML states are partitioned into MK subsets. Each of the subsets consists of the M(Lxe2x88x92K) states with the same K leading hypothesized symbols while the remaining Lxe2x88x92K hypotheses are completely different. Since the minimum-phase prefilter shifts most of the energy to the leading taps, the last Lxe2x88x92K hypotheses have little effect on the recursion metrics. To reduce computation, Lxe2x88x92K decision feedbacks are then used to select one representative state for each subset.
The same reduced state space is used by the backward recursion. Using this structure, the decision feedback side information for the backward recursion is not associated with the surviving paths in the backward trellis, but rather is determined by the forward recursion to represent backward prediction symbols along each path. That is, as shown in FIG. 2, the DFE symbols appear on the left of the MLSE symbols for both forward and backward recursions, meaning that a minimum-phase channel is appropriate for both directions. Therefore, both directions can use the same prefilter and the two concerns described in the previous section no longer apply.
The disclosed invention generalizes the traditional BCJR paradigm to this reduced-state trellis, which is referred to as a DDF-Log-MAP (delayed decision feedback Log-MAP) algorithm. The disclosed method has a forward-backward recursion structure similar to the classic Log-MAP algorithms. To reduce complexity, however, the forward recursion incorporates DDFSE to construct a reduced state space. The backward recursion then takes this state space as given, i.e., it does not hypothesize feedbacks, and computes the required soft information. The description includes exemplary applications of the invention to MPSK and M-ary differential phase-shift keying (MDPSK) modulations, respectively, with a reduced state space equivalent to that of a DDFSE with 2 MLSE taps. Generalizations to other modulations and other choices of reduced state spaces are straightforward.